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I can't think of a logical reason why Google would penalize a site without whitespace, because I'm sure its spider knows how to figure out what text is part of the visible page and ignore the rest.
If the Google engineers discovered that spammy SEO'ed websites with nothing but affiliate links often had less whitespace than quality sites, I wouldn't put it past them to penalize the sites without whitespace. BUT... I doubt there is any such correlation.